Conventionally, geostatistical software describes the pattern of spatial variation in geological properties (e.g. porosity and permeability) using a variogram model that quantifies the average of expected variability as a function of distance and direction. In reservoirs, where the geological characteristics are very continuous and easily correlated from well to well, the range (or scale), of correlation will be large and in reservoirs, where the geological characteristics change quickly over short distances, the range (or scale) of correlation will be smaller.
In certain geological environments, the range of correlation may be directionally independent. This phenomenon is very common in sedimentary environments, especially in those where the primary mechanism of transport during sediment deposition is wind or water, which results in highly channelized structures such as deltaic channels, fluvial deposits, turbidites and the like. These environments usually demonstrate a large degree of correlation variation between directions along the channel axis and perpendicular to the channel axis. The principles of conventional geostatistical practice, embedded in the majority of commercial tools for geological modeling presently available on the market, require selection of a single direction of maximum continuity, which is an average for the entire domain under study.
Traditional reservoir modeling techniques use simplified two-point statistics to represent geological structures with complex geometrical configurations, such as deltaic channels, fluvial deposits, turbidites and shale drapes. The two-point correlation is modeled through the definition of a variogram, which makes the description of the above-mentioned structures highly challenging if not impossible. One benefit of two-point geostatistical methods is their speed. One technique, for example, utilizes the Fourier-filter based method, which is described in an article written by M. Maucec, et. al. called “Streamline-based History Matching and Uncertainty: Markov-Chain Monte Carlo Study of an Offshore Turbidite Oil Field,” and is capable of generating a new realization of permeability field with large numbers of variables (˜106) within a few seconds. Although this technique is more efficient than traditional well-known algorithms, like Cholesky decomposition, it is not suitable for integration into workflows for dynamic inversion and automated history matching of reservoir models due, in part, to its dependence on the use of variogram definition.
Within the last decade, advances have been made in the form of multi-point geostatistics (MPS). MPS technology uses correlations between multiple locations at the same time to reproduce volume-variance relationship and model realizations, which are conditioned to local sample data. Examples of MPS technology combine codes like SNESIM and S-GeMS. The latter, for example, is dedicated to the local optimization of parameters involved in variogram-based models to take into account local structural characteristics of the data. MPS technology, however, still has its disadvantages such as, for example: a) dependence on the training image or training data set; and b) very long computational times for generating new geological model/realization.
More recently, Landmark Graphics has developed technology for three-dimensional volumetric modeling of geological properties using a Maximum Continuity Field (MCF). This technology is more commonly referred to as Point Vector technology, which is described in International Patent Application Publication No. WO2009/151441 and is incorporated herein by reference. The Point Vector technology introduces several advantages that enable a user to: i) direct control over local continuity directions; ii) interactively operate with “geologically intuitive” datasets, such as layering intervals, projection maps and hand drawings through a MCF; and iii) retain the maximum fidelity of a geological model by postponing the creation of a grid/mesh until the final stage of static model building immediately before integrating the static model into a dynamic model (reservoir simulator). The reservoir property modeling does not need a standard grid but only the correct distance between the points to estimate/simulate the property and the data around it.
The current Point Vector technology basically introduces a solution, commonly referred to as an “80% solution,” which is based on the approach of simply reorienting the axes of a variogram model to the local direction specified by the user. In geological structures with a high degree of local anisotropy (e.g. meandering channels), the direction of maximum continuity significantly changes locally for highly meandering channels. The 80% solution has no way of knowing how to look beyond the channel corner. The estimation of the correct distance in such geological structures requires the introduction of curvilinear distances because the minimum distance between two points in geological formations is not always a straight line (i.e. Euclidean distance) and may be curvilinear—depending on the local anisotropy field. The remaining challenges are: i) how to calculate the shortest distance between two points of interest in a grid-less model of a geological structure; and ii) which direction/orientation to use to correctly describe the local anisotropy effects.